Multi-scale Correlations Research Articles

LGIT: local–global interaction transformer for low-light image denoising

Transformer-based methods effectively capture global dependencies in images, demonstrating outstanding performance in multiple visual tasks. However, existing Transformers cannot effectively denoise large noisy images captured under low-light conditions owing to (1) the global self-attention mechanism causing high computational complexity in the spatial dimension owing to a quadratic increase in computation with the number of tokens; (2) the channel-wise self-attention computation unable to optimise the spatial correlations in images. We propose a local–global interaction Transformer (LGIT) that employs an adaptive strategy to select relevant patches for global interaction, achieving low computational complexity in global self-attention computation. A top-N patch cross-attention model (TPCA) is designed based on superpixel segmentation guidance. TPCA selects top-N patches most similar to the target image patch and applies cross attention to aggregate information from them into the target patch, effectively enhancing the utilisation of the image’s nonlocal self-similarity. A mixed-scale dual-gated feedforward network (MDGFF) is introduced for the effective extraction of multiscale local correlations. TPCA and MDGFF were combined to construct a hierarchical encoder-decoder network, LGIT, to compute self-attention within and across patches at different scales. Extensive experiments using real-world image-denoising datasets demonstrated that LGIT outperformed state-of-the-art (SOTA) convolutional neural network (CNN) and Transformer-based methods in qualitative and quantitative results.

Spatial frequency decomposition with bandpass filters for multiscale analyses and functional correlations

To address the essential problem in surface metrology of establishing functional correlations spatial, frequencies in topographic measurements are progressively decomposed into a large number of narrow bands. Bandpass filters and commercially available software are used. These bands can be analyzed with conventional surface texture parameters, like average roughness, Sa, or other parameters, for detailed, multiscale topographic characterizations. Earlier kinds of multiscale characterization, like relative area, required specialized software performing multiple triangular tiling exercises. Multiscale regression analyses can test strengths of functional correlations over a range of scales. Here, friction coefficients are regressed against standard surface texture parameters over the range of scales available in a measurement. Correlation strengths trend with the scales of the bandpass filters. Using bandpass frequency, i.e., wavelength or scale, decompositions, the R2 at 25 μm, exceeds 0.9 for Sa compared with an R2 of only 0.2 using the broader band of conventional roughness filtering. These improved, scale-specific functional correlations can facilitate scientific understandings and specifications of topographies in product and process design and in designs of quality assurance systems.

Spatio-temporal variations and multi-scale correlations of climate, water, land, and vegetation resources over the past four decades in the Heihe River Basin

Study regionHeihe River Basin (HRB), Northwest China. Study focusThe study proposes an analytical scheme to identify trend, periodicity, and scale-correlation in climate, water, land, and vegetation resources over the past four decades using multivariate remote sensing data. New hydrological insights for the regionHeat and precipitation resources in the HRB have increased at rates of 14.27℃ yr−1 and 1.26 mm yr−1, respectively. The glacier area has decreased by 47.47 %. Additionally, the increase in upstream precipitation (2.82 mm yr−1) and glacier meltwater effectively replenishes runoff, soil water, and groundwater. The implementation of the ecological water diversion project (EWDP) in 2000 has contributed to enhancing runoff and lake storage capacity. The 9.28 % increase in vegetation cover (including cropland, forest, grassland, and shrubland) indicates an improvement in the hydrothermal conditions of the HRB. Additionally, the magnitude and direction of interactions among various natural resources vary across multiple spatial scales and time scales. The effect of hydrothermal coupling on vegetation is more prominent at the interdecadal scale. Vegetation growth in the upstream area is primarily influenced by thermal condition, while moisture plays a significant role in the midstream and downstream areas. Knowledge from this study contributes to the informed allocation of natural resources and offer policymakers valuable insights to enhance eco-environmental sustainability.

Multi-layer Bundling as a New Approach for Determining Multi-scale Correlations Within a High-Dimensional Dataset

The growing complexity of biological data has spurred the development of innovative computational techniques to extract meaningful information and uncover hidden patterns within vast datasets. Biological networks, such as gene regulatory networks and protein-protein interaction networks, hold critical insights into biological features’ connections and functions. Integrating and analyzing high-dimensional data, particularly in gene expression studies, stands prominent among the challenges in deciphering these networks. Clustering methods play a crucial role in addressing these challenges, with spectral clustering emerging as a potent unsupervised technique considering intrinsic geometric structures. However, spectral clustering’s user-defined cluster number can lead to inconsistent and sometimes orthogonal clustering regimes. We propose the Multi-layer Bundling (MLB) method to address this limitation, combining multiple prominent clustering regimes to offer a comprehensive data view. We call the outcome clusters “bundles”. This approach refines clustering outcomes, unravels hierarchical organization, and identifies bridge elements mediating communication between network components. By layering clustering results, MLB provides a global-to-local view of biological feature clusters enabling insights into intricate biological systems. Furthermore, the method enhances bundle network predictions by integrating the bundle co-cluster matrix with the affinity matrix. The versatility of MLB extends beyond biological networks, making it applicable to various domains where understanding complex relationships and patterns is needed.

Bayesian hierarchical modeling for bivariate multiscale spatial data with application to blood test monitoring

Public health spatial data are often recorded at different spatial scales (or geographic regions/divisions) and over different correlated variables. Motivated by data from the Dartmouth Atlas Project, we consider jointly analyzing average annual percentages of diabetic Medicare enrollees who have taken the hemoglobin A1c and blood lipid tests, observed at the hospital service area (HSA) and county levels, respectively. Capitalizing on bivariate relationships between these two scales is not immediate as counties are not nested within HSAs. It is well known that one can improve predictions by leveraging correlations across both variables and scales. There are very few methods available that simultaneously model multivariate and multiscale correlations. We propose three new hierarchical Bayesian models for bivariate multiscale spatial data, extending spatial random effects, multivariate conditional autoregressive (MCAR), and ordered hierarchical models through a multiscale spatial approach. We simulated data from each of the three models and compared the corresponding predictions, and found the computationally intensive multiscale MCAR model is more robust to model misspecification. In an analysis of 2015 Texas Dartmouth Atlas Project data, we produced finer resolution predictions (partitioning of HSAs and counties) than univariate analyses, determined that the novel multiscale MCAR and OH models were preferable via out-of-sample metrics, and determined the HSA with the highest within-HSA variability of hemoglobin A1c blood testing. Additionally, we compare the univariate multiscale models to the bivariate multiscale models and see clear improvements in prediction over univariate analyses.

Multi-Source Information Fusion Graph Convolution Network for traffic flow prediction

As a fundamental technology in the field of intelligent transportation systems, traffic flow prediction has a wide range of applications. The utilization of Graph Convolutional Network (GCN) models is notable for capturing the complex spatial–temporal dependencies in traffic data, leading to a significant improvement in prediction accuracy. However, most existing graph construction methods overlook joint impact of auxiliary information such as weather and traffic speed on the road topology. Moreover, the research on interactions within time series at coarse temporal resolutions remains insufficiently explored, giving rise to unsatisfactory long-term prediction performance. In this study, we present a novel framework, namely Multi-Source Information Fusion Graph Convolution Network (MIFGCN), for spatial–temporal traffic flow prediction. Our key innovation lies in creating a dynamic graph that integrates weather, traffic speed, and global spatial information, effectively simulating significant traffic fluctuations caused by subtle ancillary information in the road network. Simultaneously, it captures the evolving hidden adjacency relationships between nodes over time. Furthermore, by combining with an attention-based temporal interaction module, MIFGCN learns multiscale temporal correlations at course temporal resolutions, enhancing the ability for long-term prediction. Experiments conducted on four real-world traffic datasets demonstrate that MIFGCN outperforms various state-of-the-art baselines, especially achieving a 10.50% average improvement on the PeMS08 dataset.

MSGNet: Learning Multi-Scale Inter-series Correlations for Multivariate Time Series Forecasting

Multivariate time series forecasting poses an ongoing challenge across various disciplines. Time series data often exhibit diverse intra-series and inter-series correlations, contributing to intricate and interwoven dependencies that have been the focus of numerous studies. Nevertheless, a significant research gap remains in comprehending the varying inter-series correlations across different time scales among multiple time series, an area that has received limited attention in the literature. To bridge this gap, this paper introduces MSGNet, an advanced deep learning model designed to capture the varying inter-series correlations across multiple time scales using frequency domain analysis and adaptive graph convolution. By leveraging frequency domain analysis, MSGNet effectively extracts salient periodic patterns and decomposes the time series into distinct time scales. The model incorporates a self-attention mechanism to capture intra-series dependencies, while introducing an adaptive mixhop graph convolution layer to autonomously learn diverse inter-series correlations within each time scale. Extensive experiments are conducted on several real-world datasets to showcase the effectiveness of MSGNet. Furthermore, MSGNet possesses the ability to automatically learn explainable multi-scale inter-series correlations, exhibiting strong generalization capabilities even when applied to out-of-distribution samples.

DeepMeshCity: A Deep Learning Model for Urban Grid Prediction

Urban grid prediction can be applied to many classic spatial-temporal prediction tasks such as air quality prediction, crowd density prediction, and traffic flow prediction, which is of great importance to smart city building. In light of its practical values, many methods have been developed for it and have achieved promising results. Despite their successes, two main challenges remain open: a) how to well capture the global dependencies and b) how to effectively model the multi-scale spatial-temporal correlations? To address these two challenges, we propose a novel method— DeepMeshCity , with a carefully-designed Self-Attention Citywide Grid Learner ( SA-CGL ) block comprising of a self-attention unit and a Citywide Grid Learner ( CGL ) unit. The self-attention block aims to capture the global spatial dependencies, and the CGL unit is responsible for learning the spatial-temporal correlations. In particular, a multi-scale memory unit is proposed to traverse all stacked SA-CGL blocks along a zigzag path to capture the multi-scale spatial-temporal correlations. In addition, we propose to initialize the single-scale memory units and the multi-scale memory units by using the corresponding ones in the previous fragment stack, so as to speed up the model training. We evaluate the performance of our proposed model by comparing with several state-of-the-art methods on four real-world datasets for two urban grid prediction applications. The experimental results verify the superiority of DeepMeshCity over the existing ones. The code is available at https://github.com/ILoveStudying/DeepMeshCity.

Variation in Water Deficit and Its Association with Climate Indices in Weihe River Basin, China

Based on the 24 meteorological stations in the Weihe River Basin (WRB) from 1951 to 2013, as well as the runoff data from the mainstream of the Weihe River, the temporal and spatial variations in water balance in the WRB and its relationships with runoff, the drought index, and the climate index were analyzed. The results indicate that the water balance in the WRB has been in a deficit state over the past 63 years, showing a weak declining trend with a decreasing rate of −20.04 mm/decade. Water balance is closely related to potential evapotranspiration (ET0) and precipitation (P). At the annual time scale, P plays a dominant role in water balance for 6–8 months in the WRB. The distribution of the water deficit (WD) in the WRB is uneven throughout the year, with the largest deficit occurring in June and the smallest values generally occurring in September. Furthermore, there are significant multi-scale correlations between water deficit and climate indices such as Arctic Oscillation (AO), Pacific Decadal Oscillation (PDO), and Sea Surface Temperature (SST) in the WRB. In addition, water deficit is also influenced by human activities, such as irrigation, as well as climate factors and socio-economic factors. Studying the temporal and spatial variation characteristics of water deficit and its influencing factors in the WRB is helpful toward deeply understanding the supply and demand dynamics of water resources in the basin and providing a theoretical basis and scientific guidance for the rational utilization of water resources and the high-quality development of the basin.

Estimation of soil water storage according to its multi-scale correlations with environmental factors

Soil water storage (SWS) is a crucial parameter for vegetation restoration and a variety of hydrological processes in semi-arid regions. Its dynamics reflect the integrated influence of different factors operating at various intensities and scales. In this study, we investigated the scale-specific correlations between SWS and six selected environmental factors along a 1340-m long sampling transect in a semi-arid catchment using multivariate empirical mode decomposition (MEMD). The six factors were bulk density, elevation, clay, silt, sand, and soil organic carbon content. The multivariate data series of the SWS and factors of interest were separated into seven intrinsic mode functions (IMFs) and residue. IMF1, IMF3, and IMF5 were identified as the primary scales according to the percentage of total variance (about 50%) in SWS under different soil moisture conditions. The scale-specific correlations between SWS and the corresponding factors varied with scale but were irrelevant to soil moisture condition. SWS at each IMF and residue could be estimated using the associated scale-specific environmental factors at the same IMF or residue. SWS at the measurement scale was satisfactorily estimated by summarizing all the predicted IMFs and residue, which outperformed measurement-scale SWS estimation based on multivariate stepwise linear regression between SWS and the associated factors. Soil moisture condition could affect the relative importance of the environmental factors in overall SWS estimation. In general, soil properties were the dominant predictor of SWS under different soil moisture conditions. MEMD provides a useful opportunity to deal with scale-specific correlations between various variables.

Multi-Scale CNN-Transformer Dual Network for Hyperspectral Compressive Snapshot Reconstruction

Coded aperture snapshot spectral imaging (CASSI) is a new imaging mode that captures the spectral characteristics of materials in real scenes. It encodes three-dimensional spatial–spectral data into two-dimensional snapshot measurements, and then recovers the original hyperspectral image (HSI) through a reconstruction algorithm. Hyperspectral data have multi-scale coupling correlations in both spatial and spectral dimensions. Designing a network architecture that effectively represents this coupling correlation is crucial for enhancing reconstruction quality. Although the convolutional neural network (CNN) can effectively represent local details, it cannot capture long-range correlation well. The Transformer excels at representing long-range correlation within the local window, but there are also issues of over-smoothing and loss of details. In order to cope with these problems, this paper proposes a dual-branch CNN-Transformer complementary module (DualCT). Its CNN branch mainly focuses on learning the spatial details of hyperspectral images, and the Transformer branch captures the global correlation between spectral bands. These two branches are linked through bidirectional interactions to promote the effective fusion of spatial–spectral features of the two branches. By utilizing characteristics of CASSI imaging, the residual mask attention is also designed and encapsulated in the DualCT module to refine the fused features. Furthermore, by using the DualCT module as a basic component, a multi-scale encoding and decoding model is designed to capture multi-scale spatial–spectral features of hyperspectral images and achieve end-to-end reconstruction. Experiments show that the proposed network can effectively improve reconstruction quality, and ablation experiments also verify the effectiveness of our network design.

Determinants of land use conflicts with the method of cross-wavelet analysis: Role of natural resources and human activities in spatial-temporal evolution

The imbalance and mismatch between land use structures and resource elements lead to the intensified competition for land use cover, and the resulting land use conflicts (LUCs) have attracted much attention. However, there are few studies on multi-spatial scale determinants of LUCs, due to relatively discrete scales or single determinant used in previous studies. It is a great challenge to explore the method of prioritizing research multi-scales in view of the determinants of LUCs. This study took the Shenyang Economic Zone, a developed urban agglomeration at high latitudes in China, and used cross-wavelet analysis to clarify the determinants of LUCs between natural resources and human activities in typical years (1980, 1993, 2006, and 2019). The cross-wavelet coefficients were used to extract the determinants of LUCs, and the cross-wavelet phase angles were applied to reveal the acting direction and spatial multi-scale correlation of LUCs with the determinants in the Shenyang Economic Zone. The results showed that: (1) the determinants of LUCs in the study area were distance to industrial and mining storage, intensity, soil types, digital elevation model (DEM), and landforms in 1980, were DEM and distance to industrial and mining storage in 1993, were distance to industrial and mining storage, intensity, and diversity in 2006, and were energy consumption of industrial enterprises, gross domestic product (GDP), and intensity in 2019. From 1980 to 2019, the dominant determinants influencing LUCs in the SEZ shifted from a joint influence of natural resources and human activities to dominance of human activities. (2) The action direction of LUCs with determinants had both positive and negative effects in different spatial positions. (3) The multi-scale correlations between LUCs and their determinants were obvious, and the spatial scale correlations varied significantly. The spatial scale between 94,629 and 118950 m was the most suitable spatial scale to explain the association between LUCs and determinants. The results indicated that the competition between natural resources would aggravate LUCs, however, human activities were the main cause of LUCs. Therefore, we believed that territorial spatial planning should not only consider the land distribution pattern, but also took the determinants as control variables to participate in territorial spatial planning. Our findings could provide a scientific basis for alleviating regional land contradictions and effectively allocating resource elements.

Fractal Analysis of S&P 500 Sector Indexes

In this study multifractal properties of S&P 500 sector indexes are investigated with Multifractal Detrended Fluctuation Analysis (MF-DFA). The MF-DFA is a signal processing technique that is used to describe the multifractal properties of a time series data. It is an extension of Detrended Fluctuation Analysis (DFA), which is a widely utilized method for estimating the scaling behavior of a time series. Main idea behind MF-DFA is to decompose a time series into multiple scales using a coarse-graining procedure, and then to estimate the scaling behavior of each scale using DFA. This gives a set of scaling exponents that describe the multifractal features of the time series. Our MF-DFA results indicates the presence of multifractality in all S&P 500 sector indexes. Since these indexes are multifractal, we can conclude that they possess properties such as scaling variability, nonlinear dynamics, self-similarity, long-range dependence, multiscale correlations and nonstationary.

Enhanced wave localization in multifractal scattering media

In this paper we study the structural, scattering, and wave localization properties of multifractal arrays of electric point dipoles generated from multiplicative random fields with different degrees of multiscale correlations. Specifically, using the rigorous Green's matrix method, we investigate the scattering resonances and wave localization behavior of systems with $N=10^{4}$ dipoles and demonstrate an enhanced localization behavior in highly inhomogeneous multifractal structures compared to homogeneous fractals, or monofractals. We show distinctive spectral properties, such as the absence of level repulsion in the strong multiple scattering regime and power-law statistics of level spacings, which indicate a clear localization transition enhanced in non-homogeneous multifractals. Our findings unveil the importance of multifractal structural correlations in the multiple scattering regime of electric dipole arrays and provide an efficient model for the design of multiscale nanophotonic systems with enhanced light-matter coupling and localization phenomena beyond what is possible with traditional fractal systems.

Efficient Light Field Angular Super-Resolution With Sub-Aperture Feature Learning and Macro-Pixel Upsampling

The acquisition of densely-sampled light field (LF) images is costly, which hampers the applications of LF imaging technology in 3D reconstruction, digital refocusing, virtual reality, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">etc</i> . To mitigate the obstacle, various approaches have been proposed to reconstruct densely-sampled LF images from sparsely-sampled ones. However, most existing methods still suffer from the non-Lambertian effect and large disparity issue. In this paper, we embrace the challenges by introducing a new paradigm for LF angular super-resolution (SR), which first explores the multi-scale spatial-angular correlations on the sparse sub-aperture images (SAIs) and then performs angular SR on macro-pixel features. In this way, we propose an efficient LF angular SR network, termed as EASR, with simple 3D (2D) CNNs and reshaping operations. The proposed EASR can extract effective feature representations on SAIs and can handle large disparities well by performing angular SR on macro-pixel features. Extensive comparisons with state-of-the-art methods demonstrate that our method achieves superior performance visually and quantitatively. Furthermore, our method achieves efficient angular SR by providing an excellent tradeoff between reconstruction performance and inference time. Our code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/GaoshengLiu/LF-EASR</uri>

Reconstruction of Quantitative Susceptibility Mapping from Total Field Maps with Local Field Maps Guided UU-Net.

Quantitative susceptibility mapping (QSM) is an emerging computational technique based on the magnetic resonance imaging (MRI) phase signal, which can provide magnetic susceptibility values of tissues. The existing deep learning-based models mainly reconstruct QSM from local field maps. However, the complicated inconsecutive reconstruction steps not only accumulate errors for inaccurate estimation, but also are inefficient in clinical practice. To this end, a novel local field maps guided UU-Net with Self- and Cross-Guided Transformer (LGUU-SCT-Net) is proposed to reconstruct QSM directly from the total field maps. Specifically, we propose to additionally generate the local field maps as the auxiliary supervision during the training stage. This strategy decomposes the more complicated mapping from total maps to QSM into two relatively easier ones, effectively alleviating the difficulty of direct mapping. Meanwhile, an improved U-Net model, named LGUU-SCT-Net, is further designed to promote the nonlinear mapping ability. The long-range connections are designed between two sequentially stacked U-Nets to bring more feature fusions and facilitate the information flow. The Self- and Cross-Guided Transformer integrated into these connections further captures multi-scale channel-wise correlations and guides the fusion of multiscale transferred features, assisting in the more accurate reconstruction. The experimental results on an in-vivo dataset demonstrate the superior reconstruction results of our proposed algorithm.

A joint network of non-linear graph attention and temporal attraction force for geo-sensory time series prediction.

Geo-sensory time series, such as the air quality and water distribution, are collected from numerous sensors at different geospatial locations in the same time interval. Each sensor monitors multiple parameters and generates multivariate time series. These time series change over time and vary geographically; hence, geo-sensory time series contain multi-scale spatial-temporal correlations, namely inter-sensor spatial-temporal correlations and intra-sensor spatial-temporal correlations. To capture spatial-temporal correlations, although various deep learning models have been developed, few of the models focus on capturing both correlations. To solve this problem, we propose simultaneously capture the inter- and intra-sensor spatial-temporal correlations by designing a joint network of non-linear graph attention and temporal attraction force(J-NGT) consisting two graph attention mechanisms. The non-linear graph attention mechanism can characterize node affinities for adaptively selecting the relevant exogenous series and relevant sensor series. The temporal attraction force mechanism can weigh the effect of past values on current values to represent the temporal correlation. To prove the superiority and effectiveness of our model, we evaluate our model in three real-world datasets from different fields. Experimental results show that our model can achieve better prediction performance than eight state-of-the-art models, including statistical models, machine learning models, and deep learning models. Furthermore, we conducted experiments to capture inter- and intra-sensor spatial-temporal correlations. Experimental results indicate that our model significantly improves performance by capturing both inter- and intra-sensor spatial-temporal correlations. This fully shows that our model has a greater advantage in geo-sensory time series prediction.

Graph Neural Networks for Intelligent Modelling in Network Management and Orchestration: A Survey on Communications

The advancing applications based on machine learning and deep learning in communication networks have been exponentially increasing in the system architectures of enabled software-defined networking, network functions virtualization, and other wired/wireless networks. With data exposure capabilities of graph-structured network topologies and underlying data plane information, the state-of-the-art deep learning approach, graph neural networks (GNN), has been applied to understand multi-scale deep correlations, offer generalization capability, improve the accuracy metrics of prediction modelling, and empower state representation for deep reinforcement learning (DRL) agents in future intelligent network management and orchestration. This paper contributes a taxonomy of recent studies using GNN-based approaches to optimize the control policies, including offloading strategies, routing optimization, virtual network function orchestration, and resource allocation. The algorithm designs of converged DRL and GNN are reviewed throughout the selected studies by presenting the state generalization, GNN-assisted action selection, and reward valuation cooperating with GNN outputs. We also survey the GNN-empowered application deployment in the autonomous control of optical networks, Internet of Healthcare Things, Internet of Vehicles, Industrial Internet of Things, and other smart city applications. Finally, we provide a potential discussion on research challenges and future directions.

Strength Deterioration Model of Soft Rock Considering Mesoscopic Bonding–Expansion Coupling Mechanism under Freeze–Thaw Cycles

The mechanical deterioration of soft rocks under freeze–thaw cycles is caused by the accumulation of mesoscopic damage. However, the current freeze–thaw deterioration model for soft rocks does not adequately consider the multiscale correlations, which makes the strength calculation results differ greatly from the test results and cannot fully reveal the damage mechanism of soft rocks under freeze–thaw cycling conditions. In this paper, the bond damage and pore ice expansion laws are considered from the soft-rock mesoscopic bond unit and a multiscale strength deterioration model is proposed. The freeze–thaw deterioration model is extended to intact and cracked soft rocks by the Discrete Element Method (DEM). The results are validated by laboratory tests. The peak strengths of intact soft rocks are calculated within 10% error for different numbers of freeze–thaw cycles, and the macroscopic crack development simulation results are consistent with the laboratory tests. The joints have a significant effect on the damage evolution: the freeze–thaw-induced mesoscopic damage in cracked rocks accumulates at a uniform rate, while the damage in intact soft rocks grows exponentially; the freeze–thaw cracks in cracked soft rocks are distributed between 60 and 90°, with a tensile–shear damage ratio of 1:2; the freeze–thaw cracks in intact soft rocks are distributed around 90°, with a tensile–shear damage ratio of 1:3. The deterioration model proposed in this paper can fully consider the multiscale damage correlations, which renders it easy to promote the application in the freeze–thaw hazard problem of soft rock engineering.

Wavelet Multiscale and Spillover Analyses of Volatility and Correlation

This article investigates the dynamic empirical relationships among realized, risk-neutral, and risk premium measures of volatility and correlation of the S&amp;P 500 stock index from January 1, 2000, to December 31, 2020. The empirical investigation runs a spillover analysis to identify the receiver and the transmitter variables and implements a wavelet local multiple correlation (WLMC) methodology to study the multiscale correlations. The results identify the implied measures as the most influential variables and also reveal that the strength of correlation is changing with time scales; moreover, the correlation between volatility risk premium and correlation risk premium is not always statistically significant through either time scales or time periods. These findings support the use of scale-based correlation metrics in derivatives studies.